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The fundamental ideas used earlier to obtain estimates of
elastic constants by using the analytical structure of the bounds
(by making informed approximations for the elastic constants) can again be
used for effective conductivity. The ideas are virtually the same, but
somewhat easier to apply since we have only one constant to estimate,
not two. Since we are now dealing with the Beran bounds on
two-component media that depend specifically on the average
, we want to define again the geometric mean
| |
(33) |

Then we will have an estimator for a new transform variable that lies
between the transform variables of the rigorous bounds according to
| |
(34) |

The properties of the canonical function guarantee that
| |
(35) |

** Next:** Conductivity for random polycrystals
** Up:** CONDUCTIVITY: CANONICAL FUNCTIONS AND
** Previous:** Canonical functions
Stanford Exploration Project

5/3/2005